实二次曲面上O（p，q）对角作用的共形协变微分算子
Conformally covariant differential operators for the diagonal action of O(p, q) on real quadrics
摘要：
设$X=G/P$是实射影二次曲面，其中$G=O(p,q)$和$P$是$G$的抛物子群.设$\left(π_{λ,ε}, \mathcal{H}_{λ,ε}\right)_{ (λ,ε)\in \mathbb {C}\times \{\pm\}}$是由$P$的特征标导出的$G$的（光滑）表示族.对于$(λ, ε), (μ, η)\in \mathbb{C} \times \{\pm\}$，构造了$X\times X$上的一个微分算子$\mathbf{D}_{(λ,ε), (μ,η)}^{reg}$，它将$G$ -协变地从$\mathcal{H}_{λ,ε} \otimes \mathcal{H}_{μ, η}$作用到$\mathcal{H}_{λ+1,-ε} \otimes \mathcal{H}_{μ+1, -η}$.
英文摘要：
Let $X=G/P$ be a real projective quadric, where $G=O(p,q)$ and $P$ is a parabolic subgroup of $G$. Let $\left(π_{λ,ε}, \mathcal{H}_{λ,ε}\right)_{ (λ,ε)\in \mathbb {C}\times \{\pm\}}$ be the family of (smooth) representations of $G$ induced from the characters of $P$. For $(λ, ε), (μ, η)\in \mathbb{C} \times \{\pm\}$, a differential operator $\mathbf{D}_{(λ,ε), (μ,η)}^{reg}$ on $X\times X$, acting $G$-covariantly from $\mathcal{H}_{λ,ε} \otimes \mathcal{H}_{μ, η}$ into $\mathcal{H}_{λ+1,-ε} \otimes \mathcal{H}_{μ+1, -η}$ is constructed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
